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Mathematics

I have noticed a significant decline over the years in the ability of my students to estimate quantities, and have attributed it to an increased reliance on calculators and computers, but it may be a consequence of more subtle differences in brain development.

Like Malcolm Gladwell s Tipping Point , Nassim Taleb s Black Swan threatens to become a permanent part of the lexicon. In this best-selling book, he makes the argument that evolution has prepared us to over-emphasize continuous, Gaussian relationships because they occur much more frequently than do rare but momentous, unpredictable events.

Back in the 1960's, I was captivated by "Percentage Baseball" by Earnshaw Cook. Now long out of print and a collector's item, this book was a forerunner of the "science" of SABRmetrics (after the Society for American Baseball Research) that refers to the scientific (statistical) evaluation of the game.

In 1900, David Hilbert gave an address to the International Congress of Mathematicians that outlined the twenty three most important unsolved problems of mathematics, as he saw them. In "The Honors Class", Benjamin Yandell describes the problems and the very remarkable people who worked on them.

When nearly a dozen scientists, all in some way associated with research on biotechnology, die within a year of the 9/11 attacks, can it be coincidence? Yes, says Lisa Belkin, author of this excellent article on one of the constants of pseudoscience, the attribution of "cause" to random events.

I have to admit that I haven't finished reading this book. With over six hundred, large-format pages and relatively small type, it would probably not have made "Hal's Picks" until next year if I had waited until I had completed it. However, it is entirely possible to dip in for a chapter here and a chapter there.

In about 1637, a French mathematical genius named Pierre de Fermat wrote in the margin of his copy of Arithmetica by Pythagorus, that he could prove that there were no solutions to the simple variation on Pythagorus' Theorem, az + bz = czwhen a, b, and c are integers and z is larger than two.

Physicist J. Richard Gott of Princeton published a provocative article in Nature back in 1993, that described a simple method for the estimation of the likely lifetime of "things" on the basis solely of the length of their existence to date.